Method and apparatus for checking the response of a transconductance- capacitance filter

ABSTRACT

A transconductance-capacitance filter having a plurality of transconductors, that operates in a normal operation mode and a testing/tuning operation mode. During the normal operation mode, the transconductors operate as having normal transconductances. During the testing/tuning operation mode, the transconductances are scaled by a same amount, so that frequencies of the test signals provided are lower than in the normal operation mode, and so that transfer characteristics of the filter can be easily verified.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a transconductance-capacitancefilter, and a method of verifying transfer characteristics in atransconductance-capacitance filter. More particularly, the presentinvention relates to a transconductance-capacitance filter, and a methodof verifying the transfer characteristic of a high-frequency integratedcontinuous-time filter of a transconductance-capacitance (gm-C) type.

[0003] 2. Description of the Background Art

[0004] The four basic linear operations (integration, scaling,summation, inversion) used to synthesize a large class of transferfunctions can be easily implemented using only transconductors andcapacitors. For example, a transconductor loaded with a capacitor actsas a voltage input—voltage output integrator. Scaling is done bychanging the transconductance of the tranconductor and/or thecapacitance of the load capacitor. The output currents of a plurality oftransconductors can be summed by tying the outputs to a same node. Also,inversion can be done for instance by crossing inputs of atranconductor.

[0005] The basic building block of a transconductance-capacitance filteris a multiple input transconductance-capacitance integrator. This blockcan perform all of the above noted basic operations. The filter appearsas a collection of interconnected multiple inputtranconsconductance-capacitance integrators. In an integrated circuit,both the transconductance of the transconductor and the capacitance ofthe capacitor are subject to influences such as fabrication processes,power supply and temperature variations. Thus, it is required to checkthe conformity of the implemented transfer function and to tune thefilter so as to fulfill the designed function. Most of the tuning effortis directed toward adjusting the transconductance of thetransconductors.

[0006] One of the conventional direct methods of checking the transferfunction of a continuous-time filter consists of applying a constantamplitude, variable (sweeping) frequency sinusoidal signal at the inputof the filter and measuring the amplitude and the phase of the resultingwaveform at the output of the filter. Indirect methods, in contrast,analyze the step response of the filter. These known methods require thegeneration of a test signal (either on-chip or off-chip), applying thetest signal at the input of the circuit under test (CUT), and readingand processing the response of the circuit. This can be done eitheron-chip or off-chip. For tuning purposes, the response of the filter isused in a feedback configuration to adjust its parameters.

[0007] FIGS. 1-5 are block diagrams showing circuit configurations ofconventional checking methods. FIG. 1 is a block diagram showing atesting circuit 100 for an integrated filter with an external testsignal source 105 and an external generic analyzer 145. As shown in FIG.1, the testing circuit 100 includes an input buffer 110 coupled to theoutput of external test signal source 105, a circuit under test (CUT)115, an output buffer 140 that provides an output to external analyzer145, first switch 130 connected between input buffer 110 and CUT 115,second switch 135 connected between CUT 115 and output buffer 140, andan internal circuit 120 connected to receive a signal from second switch135 and to provide a signal to first switch 130. In this circuit, inputbuffer 110, CUT 115, internal circuit 120, first and second switches 130and 135, and output buffer 140 are all formed on a semiconductor chip150, while the external test signal source 105 and the external analyzer145 are formed off the chip 150.

[0008] The CUT 115 can be connected through the first and secondswitches 130 and 135 either to the internal circuit 120, or to the inputand output buffers 110 and 140. When connected to input and outputbuffers 110 and 140 by first and second switches 130 and 135, CUT 115 isconnected to the external test signal source 105 and the externalanalyzer 145. The first and second switches are controlled by switchingsignals SW. The switching signals SW indicate either a normal operationstate (connecting the switches 130 and 135 to normal nodes N), or a testoperation state (connecting the switches 130 and 135 to test nodes T).

[0009]FIG. 2 is a block diagram showing a testing circuit 200 for anintegrated filter that is similar to the circuit shown in FIG. 1.However, an external analog-to-digital converter (ADC) 255 and digitalsignal processor (DSP) 260 are included in place of external analyzer145 of FIG. 1. The testing circuit 200 of FIG. 2 is thus similar to thetesting circuit 100 of FIG. 1, but the analyzer device is DSP-based. Inthis circuit shown in FIG. 2, input buffer 110, CUT 115, internalcircuit 120, first and second switches 130 and 135, and output buffer140 are all formed on a semiconductor chip 250, while the external testsignal source 105, the external ADC 255, and the external DSP 260 areformed off chip 250. The external ADC 255 of the testing circuit 200acts as the interface between the CUT 115 and the DSP 260. Since the ADC255 is external, it can also be used for other functions external to thechip 250.

[0010]FIG. 3 is a block diagram showing a testing circuit 300 for anintegrated filter that is similar to the circuit shown in FIG. 2.However, an internal ADC 355 is provided on the semiconductor chip 350,in place of output buffer 140 of FIG. 2. Also, external ADC 255 of FIG.2 is not included in the circuit as shown in FIG. 3. The internal ADC355 is coupled to receive an output from second switch 135 and providesan output directly to external DSP 260. Internal ADC 355 is dedicated totest/tuning purposes. In this circuit as shown in FIG. 3, input buffer110, CUT 115, internal circuit 120, first and second switches 130 and135, and internal ADC 355 are all formed on semiconductor chip 350,while the external test signal source 105 and the external DSP 260 areformed off chip 350. Since the internal ADC 355 is disposed onsemiconductor chip 350, there is no need for an analog output buffer onchip 350 for testing the CUT 115. In operation, the chip 350 receives ananalog test signal, and outputs a digital test signal.

[0011]FIG. 4 is a block diagram showing a testing circuit 400 for anintegrated filter that is similar to the circuit shown in FIG. 3.However, internal test signal source 405 is provided on semiconductorchip 450, in place of external test signal source 105 of FIG. 3.Internal test signal source 405 provides a test signal directly to firstswitch 130. Input buffer 110 of FIG. 3 is not included in the circuit asshown in FIG. 4. Also, an internal DSP 460 is provided on chip 450, inplace of external DSP 260 of FIG. 3. Internal DSP 460 directly receivesan output of internal ADC 355. Internal DSP 460 is dedicated totest/tuning purposes. In this circuit as shown in FIG. 4, internal testsignal source 405, CUT 115, internal circuit 120, first and secondswitches 130 and 135, internal ADC 355, and internal DSP 460 are allformed on semiconductor chip 450. Since the signal source 405 and theADC 355 are both internal, there is no need for input and output bufferson chip 450 for testing the CUT 115. In operation, chip 450 generatesinput signals internally, and outputs a digital signal.

[0012]FIG. 5 is a block diagram showing a testing circuit 500 for anintegrated filter that is similar to the circuit shown in FIG. 4.However, CUT 115 and internal ADC 555 are formed on main circuit 570. Inother words, the internal ADC 355 of FIG. 4 is moved to be part of maincircuit 570 as shown in FIG. 5. Internal ADC 555 receives an outputdirectly from CUT 115, and provides an output to second switch 135. Aspreviously, CUT 115 receives an input from first switch 130. In thecircuit of FIG. 5, the internal ADC 555 is part of main circuit 570, andis shared as for normal operation with internal circuit 120 and as fortest/tuning. In this circuit of FIG. 5, internal test signal source 405,main circuit 570, internal circuit 120, first and second switches 130and 135, and internal DSP 460 are all formed on semiconductor chip 550.

[0013] In the testing circuit 500 of FIG. 5, internal ADC 555 is part ofmain circuit 570, and operates with CUT 115 during normal operation. Inother words, when the switch signals SW indicate a normal mode (i.e.,connecting the switches 130 and 135 to the normal nodes N), the internalcircuit 120 is connected to both internal ADC 555 and CUT 115, so thatinternal circuit 120 uses internal ADC 555 during normal operation.

[0014] However, providing an external high-frequency test signal to achip and channeling the external high-frequency test signal to the inputof CUT 115 as in FIGS. 1-3, is an operation prone to errors because ofparasitic elements, noise, DC offset and non-linear behavior ofinterface blocks. Extracting the response of the circuit requiresinterface blocks that must be able to drive external pads while keepingthe loading of the CUT 115 at a minimum.

[0015] On the other hand, generating a high-frequency test/tuning signalon-chip as in FIGS. 4 and 5 requires special circuitry, such as alow-noise, accurately controlled amplitude sinusoidal oscillator.Furthermore, reading of the high-frequency response on-chip requireseither special analog blocks such as precision amplitude discriminators,or an on-chip high-speed analog-to-digital converter (ADC) as well ason-chip or off-chip digital signal processing (DSP) capabilities. In thelatter case, high-speed digital communication with the external testequipment is required.

[0016] It is therefore desirable to provide an easier to implementmethod of testing the transfer characteristic of a high-frequencyintegrated continuous-time filter.

SUMMARY OF THE INVENTION

[0017] The present invention is therefore directed to atransconductance-capacitance filter, and a method of verifying thetransfer characteristics of a high-frequency integrated continuous-timefilter of a tranconductance-capacitance type, that substantiallyovercome one or more of the problems due to the limitations anddisadvantages of the related art.

[0018] It is thus an object of the present invention to overcome or atleast minimize the various drawbacks associated with conventionaltechniques for testing the transfer characteristic of a high-frequencyintegrated continuous-time filter.

[0019] In accordance with this invention, a transconductance-capacitanceintegrator is provided that includes a plurality of transconductors thatprovide transconductor output currents; a current follower that providesan output current; a capacitor, coupled to the current follower, thatprovides an output voltage of the transconductance-capacitanceintegrator responsive to the output current; a scaling circuit thatscales the transconductor output currents of the plurality oftransconductors by a same scaling factor to provide a scaledtransconductor output current; and a mode switch that is operable in atest/tuning operation mode to provide the scaled transconductor outputcurrent to the current follower and in a normal operation mode toprovide the transconductor output current to the current follower.

[0020] The transconductors preferably have a first transconductance inthe normal operation mode, and have a second transconductance in thetest/tuning operation mode. In this case, the second transconductancemay be obtained by dividing the output currents of the transconductors.

[0021] In test/tuning mode, the output currents of all of thetransconductors may be divided by the same ratio.

[0022] The second transconductances may be obtained by dividing theoutput currents of the transconductors through resistive dividers.

[0023] Also in accordance with this invention, a method of verifying atransfer function of a tranconductance-capacitance filter including aplurality of transconductors that provide transconductor outputcurrents, includes converting the transconductor output currents into afirst set of output voltages during a normal operation mode of thetransconductance-capacitance filter; and scaling the transconductoroutput currents by a scaling factor to provide a set of scaledtransconductor output currents and converting the set of scaledtransconductor output currents into a second set of output voltages forverifying the transfer function, during a test/tuning operation mode ofthe transconductance-capacitance filter.

[0024] Also in further accordance with this invention, a direct on-chipclosed loop tuning system includes a first filter having a plurality offirst transconductors that provide a first set of transconductorcurrents, a first set of adders that add the first transconductorcurrents to provide a first set of transconductor output currents and afirst set of scalers that scale the set of first transconductor outputcurrents to provide a set of scaled first transconductor outputcurrents, the first filter being operable in a normal operation mode tooutput a first set of first transconductor output currents and in atest/tuning operation mode to output a set of scaled firsttransconductor output currents; a second filter having a plurality ofsecond transconductors that provide a second set of transconductorcurrents, a second set of adders that add the second set oftransconductor currents to provide a set of second transconductor outputcurrents and a second set of scalers that scale the second set oftransconductor output currents to provide a scaled second set oftransconductor output currents, the second filter being operable in thenormal operation mode to output a set of second transconductor outputcurrents and in the test/tuning operation mode to output the scaled setof second transconductor output currents; and a controller thatsimultaneously switches one of the first and second filters into thenormal operation mode and another of the first and second filters intothe test/tuning operation mode.

[0025] Further scope of applicability of the present invention willbecome apparent from the detailed description given hereinafter.However, it should be understood that the detailed description andspecific examples, while indicating preferred embodiments of theinvention, are given by way of illustration only, since various changesand modifications within the spirit and scope of the invention willbecome apparent to those skilled in the art from this detaileddescription.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The present invention will become more fully understood from thedetailed description given hereinbelow and the accompanying drawingswhich are given by way of illustration only, and thus are not limitativeof the present invention, and wherein:

[0027]FIG. 1 is a block diagram showing a conventional circuit fortesting an integrated filter, including an external test signal sourceand an external generic analyzer;

[0028]FIG. 2 is a block diagram showing a conventional circuit fortesting an integrated filter, including an external test signal source,an external ADC and an external DSP-based analyzer;

[0029]FIG. 3 is a block diagram showing a conventional circuit fortesting an integrated filter, including an external test signal source,an internal ADC for testing, and an external DSP-based analyzer;

[0030]FIG. 4 is a block diagram showing a conventional circuit fortesting an integrated filter, including an internal test signal source,an internal ADC for testing, and an internal DSP-based analyzer;

[0031]FIG. 5 is a block diagram showing a conventional circuit fortesting an integrated filter, including an internal test signal source,an ADC as part of a main circuit, and an internal DSP-based analyzer;

[0032]FIG. 6 is a circuit diagram of a multiple input transconductorwith a current adder and a current follower (GMA);

[0033]FIG. 7 is a circuit diagram of a multiple input transconductorwith a current adder, a resistive current divider, and a currentfollower (SGMA);

[0034]FIG. 8 is a circuit diagram of a voltage input-voltage outputmultiple input transconductance-capacitance continuous-time integrator(GMAC);

[0035]FIG. 9 is a circuit diagram of a scaled voltage input-voltageoutput transconductance-capacitance multiple input continuous-timeintegrator (SGMAC);

[0036]FIG. 10 is a circuit diagram of a second order, continuous-timetransconductance-capacitance filter built with GMAC cells;

[0037]FIG. 11 is a circuit diagram of a second order, continuous-timetransconductance-capacitance filter built with SGMAC cells;

[0038]FIGS. 12A and 12B are graphs of normal and scaled magnitude andphase characteristics for a second order low-pass Butterworth filter;

[0039]FIG. 13A is a circuit diagram of a “k” input CSGMAC;

[0040]FIG. 13B is a circuit diagram of a second order filter usingCSGMACs in the test/tuning mode according to a first preferredembodiment of the present invention;

[0041]FIG. 14 is a block diagram showing a circuit for testing anintegrated filter using CSGMACs in the test mode;

[0042]FIG. 15 is a block diagram showing a circuit for a standard directon-chip closed-loop tuning subsystem; and

[0043]FIG. 16 is a block diagram showing a circuit for a direct on-chipclosed-loop tuning subsystem using CSGMACs in the tuning mode.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0044] In an effort to solve the problems listed above, this inventionprovides a method and circuit for measuring frequency response, themethod and circuit being useful for checking the integrity of the filtercircuit and/or for tuning purposes.

[0045] The preferred embodiments of the invention involve maintaining aregular filter transconductance for normal operation, but scaling downall the transconductances of the filter by the same factor for testingand/or tuning purposes. Thus, the transconductances of the filter areall scaled down by the same factor m, through resistive dividers forexample. This scaling down of transconductances is the equivalent ofscaling up all the capacitances of the chip by the same factor m.

[0046] The magnitude and the phase of the frequency response of thescaled-down filter will retain the shape of the correspondingcharacteristics of the normal operation filter, but will be in acorrespondingly reduced frequency domain. The relatively low frequencyoutput signal of the scaled-down filter is easier to measure on-chip, orto extract and measure off-chip.

[0047] The preferred embodiments provide a low cost, low area penaltyapproach to significantly reduce the drawbacks associated with themeasurements of high frequency characteristics. In the preferredembodiments, the frequencies that must be measured can be reduced fromtens of MHz down to one MHz or lower. For systems that include ananalog-to-digital converter (ADC) in the same signal path as the filterto be tested, for instance systems where the filter is used foranti-aliasing purposes in front of the ADC, the response of thescaled-down analog filter can be digitized on chip and processed on-chipor off-chip at a lower speed.

[0048] By dividing all the output currents injected by thetransconductors into the corresponding capacitors by the same factor m,the corresponding capacitors in the transfer function of the filterappear as if multiplied by the factor m. Since the output currents ofall the relevant transconductances of the filter are divided by the samefactor m, the magnitude and phase characteristics of the filter willhave a similar shape but will be translated to a lower frequency.

[0049] It is to be understood that the following concepts of thepreferred embodiments are generally applicable to filters of variousorders and configurations. However, for purposes of illustration only,second-order filter sections are considered in the preferredembodiments. Also, the building blocks of thetransconductance-capacitance filters of the preferred embodiments are atransconductor, a current adder and a capacitor. A generictransconductor with a current adder (a GMA) is considered with referenceto FIG. 6, for the case of two transconductors.

[0050]FIG. 6 is a circuit diagram of a multiple input transconductorwith a current follower (GMA). As shown in FIG. 6, the GMA 600 includesfirst and second transconductors 605 and 610, and a current follower620. Output currents i_(g1) and i_(g2) from first and secondtransconductors 605 and 610 are provided to current follower 620.

[0051] The first and second transconductors 605 and 610 respectivelyhave first and second transconductances g_(m1) and g_(m2), and inputvoltages v_(in1) and v_(in2) respectively input thereto. First andsecond transconductors 605 and 610 are differential inputvoltage-to-current converters, ideally having infinite input and outputimpedances. The output currents i_(g1) and i_(g2) of the first andsecond transconductors 605 and 610, respectively, are determined by thefollowing equations:

i _(g1) =g _(m1) ·v _(in1)  (1),

and

i _(g2) =g _(m2) ·v _(in2)  (2),

[0052] where g_(m1) is the transconductance of the first transconductor605, g_(m2) is the transconductance of the second transconductor 610,v_(in1) is the input voltage of the first transconductor 605, andv_(in2) is the input voltage of the second transconductor 610. Thecurrent follower 620, which ideally has zero input impedance andinfinite output impedance, adds the first and second output currentsi_(g1) and i_(g2) and provides the output current i_(out1) according tothe following equation:

i _(out1) =i _(g1) +i _(g2) =g _(m1) ·v _(in1) +g _(m2) ·v _(in2)  (3).

[0053] The output current i_(out1) of a GMA can be scaled by the use ofa current divider between a summing point of the transconductors and thezero input impedance of the current follower. An example of such ascaled output current GMA (or SGMA) is shown in FIG. 7. FIG. 7 is acircuit diagram of a multiple input transconductor with a current adder,a resistive divider, and a current follower. As shown in FIG. 7, theSGMA 700 includes first and second transconductors 605 and 610, acurrent follower 720, and a resistive divider 730. The resistive divider730 is disposed between the first and second transconductors 605 and 610and the current follower 720, and includes first and second resistors R₁and R₂ for example. That is, first and second output currents i_(g1) andi_(g2) are combined at node A to provide transconductance current i_(g).The first ends of first and second resistors R_(1 and R) ₂ are coupledto transconductor current i_(g). A second end of the second resistor R₂is coupled to a respective input of current follower 720. A second endof first resistor R₁ is coupled to ground, and another respective inputof current follower 720 is also coupled to ground.

[0054] The output current i_(out2) of the SGMA 700 is determined by theformula: $\begin{matrix}{{i_{out2} = {\frac{R_{1}}{R_{1} + R_{2}} \cdot ( {{g_{m1} \cdot v_{in1}} + {g_{m2} \cdot v_{in2}}} )}},} & (4)\end{matrix}$

[0055] where R₁ is the resistance of the first resistor and R₂ is theresistance of the second resistor. Thus, the output current i_(out2) ofthe SGMA 700 is similar to the output current i_(out1) of the GMA 600,except that the output current i_(out2) of the SGMA 700 is scaled downby the resistive divider 730.

[0056] The basic building block of a continuous-timetransconductance-capacitance filter is a voltage input-voltage outputintegrator built out of a GMA loaded with a capacitor (GMAC). FIG. 8 isa circuit diagram of such a voltage input-voltage outputtransconductance-capacitance continuous-time integrator (GMAC). As shownin FIG. 8, the GMAC 800 includes first and second transconductors 605and 610, and a current follower 820, configured somewhat similarly as inFIG. 6. However, capacitor C is connected to the output of the currentfollower 820 to convert the output current i_(out1) to an output voltagev_(out1).

[0057] A scaled GMA driving an output capacitor is hereinafter called anSGMAC. FIG. 9 is a circuit diagram of a scaled voltage input-voltageoutput transconductance-capacitance continuous-time integrator (SGMAC).As shown in FIG. 9, the SGMAC 900 includes first and secondtransconductors 605 and 610, a current adder, a current follower 920, aresistive divider 730 and a capacitor C coupled to the output of currentfollower 920. Resistive divider 730 is configured, and coupled to thesum of transconductor currents i_(g) provided from node A and currentfollower 920, in a similar manner as featured in FIG. 7. As with GMAC800 of FIG. 8, capacitor C in SGMAC 900 is connected to the output ofthe current follower 730, to convert the output current i_(out1) to anoutput voltage v_(out1).

[0058] An SGMAC may be implemented using multiple differential pairsinjecting current through resistive dividers into a capacitor loadedfolded-cascode stage as the current follower. Since the input impedanceof the real folded-cascode is greater than zero, the equivalentresistance of the resistive divider should be large enough as not tosignificantly affect the accuracy of the current division.

[0059]FIG. 10 shows a continuous-time transconductance-capacitancefilter 1000 built with GMAC cells. The disclosed filter 1000 is a secondorder filter, i.e., a biquad filter. The filter of FIG. 10 includes athree-transconductor GMAC 1001 and a single-transconductor GMAC 1002formed together in a feedback loop. As shown in FIG. 10, thethree-transconductor GMAC 1001 includes a first input transconductor1005 having input voltage v_(in1) applied thereto, an adder 1050 coupledto an output of first input transconductor 1005, and a first currentfollower 1020 coupled to an output of adder 1050. A first capacitor C₁is coupled to the output of first current follower 1020. A firstfeedback transconductor 1040 is coupled to a first end of firstcapacitor C₁, and provides and output to adder 1050. A second feedbacktransconductor 1045 also provides an output to adder 1050. Thesingle-transconductor GMAC 1002 includes a second input transconductor1010 that is coupled to the first end of first capacitor C₁. A secondcurrent follower 1025 is connected to an output of second inputtransconductor 1010. A second capacitor C₂ is connected to the output ofsecond current follower 1025. Also, an output of second current follower1025 at a first end of second capacitor C₂ is provided to secondfeedback transconductor 1045.

[0060] The transfer function T(s) of the filter 1000 relative to theinput voltage v_(in) and the output v_(out) is shown by the equation:$\begin{matrix}{{{T(s)} = {\frac{V_{out}(s)}{V_{in}(s)} = \frac{g_{m1} \cdot g_{m2}}{{( {C_{1} \cdot C_{2}} ) \cdot s^{2}} + {( {g_{m3} \cdot C_{2}} ) \cdot s} + ( {g_{m2} \cdot g_{m4}} )}}},} & (5)\end{matrix}$

[0061] where s is the complex frequency variable, V_(out)(s) is theLaplace transform of the output voltage, V_(in)(s) is the Laplacetransform of the input voltage, g_(m1) is the transconductance of thefirst input transconductor 1005, g_(m2) is the transconductance of thesecond input transconductor 1010, g_(m3) is the transconductance of thefirst feedback transconductor 1040, g_(m4) is the transconductance ofthe second feedback transconductor 1045, C₁ represents the capacitanceof the first capacitor, and C₂ represents the capacitance of the secondcapacitor.

[0062] The main parameters of the filter 1000 are the DC gain T(0), thecut-off frequency ω₀, and the quality factor Q, which are determined bythe following equations: $\begin{matrix}{{{T(0)} = \frac{g_{m1}}{g_{m4}}},} & (6) \\{{\omega_{0} = \sqrt{\frac{g_{m2} \cdot g_{m4}}{C_{1} \cdot C_{2}}}},{and}} & (7) \\{Q = {\sqrt{\frac{g_{m2} \cdot g_{m4}}{g_{m3}^{2}} \cdot \frac{C_{1}}{C_{2}}}.}} & (8)\end{matrix}$

[0063]FIG. 11 is a circuit diagram of a second order, continuous-timetransconductance-capacitance filter built with SGMAC cells. The biquadfilter 1100 of FIG. 11 is similar to the biquad filter 1000 shown inFIG. 10, except that the GMACs in FIG. 10 have been replaced by SGMACsin FIG. 11. That is, filter 1100 is also a second order filter, andincludes a three-transconductor SGMAC 1101 and a single-transconductorSGMAC 1102 formed together in a feedback loop.

[0064] As shown in FIG. 11, the three-transconductor SGMAC 1101 includesall the elements of the GMAC 1001 in FIG. 10, in addition to including afirst resistive divider 1130 coupled between adder 1050 and firstcurrent follower 1020. The single-transconductor SGMAC 1102 includes allthe elements of the GMAC 1002 in FIG. 10, in addition to including asecond resistive divider 1135 coupled between second inputtransconductor 1010 and second current follower 1025. The firstresistive divider 1130 includes first resistors R₁₁ and R₁₂ having firstends coupled to an output of adder 1050. A second end of resistor R₁₂ iscoupled to a corresponding input of first current follower 1020. Asecond end of resistor R₁₁ is coupled to ground, along with anothercorresponding input of first current follower 1020. The second resistivedivider 1135 includes second resistors R₂₁ and R₂₂ having first endscoupled to an output of second input transconductor 1010. A second endof resistor R₂₂ is coupled to a corresponding input of second currentfollower 1025. A second end of resistor R₂₁ is coupled to ground, alongwith another corresponding input of second current follower 1025.

[0065] The output currents of the SGMACs are scaled by the same amount,α, as shown in the following equation: $\begin{matrix}{{\alpha = {\frac{R_{11}}{R_{11} + R_{12}} = \frac{R_{21}}{R_{21} + R_{22}}}},} & (9)\end{matrix}$

[0066] where R₁₁ and R₁₂ are the resistances of the first resistors andR₂₁ and R₂₂ are the resistances of the second resistors.

[0067] As a result of the resistive dividers 1130 and 1135, the outputcurrents of the first and second current followers 1020 and 1025 arescaled by a factor of α, compared to the outputs of the currentfollowers in the circuit 1000 of FIG. 10. The transfer function T(s) ofthe filter of FIG. 11 is determined by the equations: $\begin{matrix}{{{T^{\prime}(s)} = {\frac{V_{out}(s)}{V_{in}(s)} = \frac{\alpha^{2} \cdot ( {g_{m1} \cdot g_{m2}} )}{{( {C_{1} \cdot C_{2}} ) \cdot s^{2}} + {\alpha \cdot ( {g_{m3} \cdot C_{2}} ) \cdot s} + {\alpha^{2} \cdot ( {g_{m2} \cdot g_{m4}} )}}}},{and}} & (10) \\{{T^{\prime}(s)} = {\frac{V_{out}(s)}{V_{in}(s)} = {\frac{g_{m1} \cdot g_{m2}}{{( {\frac{C_{1}}{\alpha} \cdot \frac{C_{2}}{\alpha}} ) \cdot s^{2}} + {( {g_{m3} \cdot \frac{C_{2}}{\alpha}} ) \cdot s} + {g_{m2} \cdot g_{m4}}}.}}} & (11)\end{matrix}$

[0068] The filter 1100 of FIG. 11 is called a constant-capacitancescaled filter. Furthermore, because the same scaling factor is used forall of the transconductors, the circuit 1100 of FIG. 11 appears as ascaled capacitance version of the circuit 1000 of FIG. 10, from thetransfer characteristic viewpoint.

[0069] The main parameters of the filter of FIG. 11 are the DC gainT′(0), the cut-off frequency ω₀′, and the quality factor Q′, which areshown by the following equations: $\begin{matrix}{{{T^{\prime}(0)} = {\frac{\alpha \cdot g_{m1}}{\alpha \cdot g_{m4}} = {\frac{g_{m1}}{g_{m4}} = {T(0)}}}},} & (12) \\{{\omega_{0}^{\prime} = {\sqrt{\frac{\alpha \cdot g_{m2} \cdot \alpha \cdot g_{m4}}{C_{1} \cdot C_{2}}} = {\alpha \cdot \omega_{0}}}},{and}} & (13) \\{Q^{\prime} = {\sqrt{\frac{( {\alpha \cdot g_{m2}} ) \cdot ( {\alpha \cdot g_{m4}} )}{( {\alpha \cdot g_{m3}} )^{2}} \cdot \frac{C_{1}}{C_{2}}} = {Q.}}} & (14)\end{matrix}$

[0070] From these equations, it should be understood that the frequencyresponse of the scaled filter maintains the shape of the originalcircuit, but at a lower frequency.

[0071] An illustration of this frequency scaling is presented in FIGS.12A and 12B for a second-order low-pass Butterworth filter with anominal cut-off frequency of 25 MHz and a scaled-down frequency of 2.5MHz (i.e., α=0.1). In particular, FIG. 12A shows the magnitude versusfrequency for the nominal cut-off frequency and the scaled-down cut-offfrequency, and FIG. 12B shows the phase shift versus frequency for thenominal frequency and the scaled-down frequency.

[0072] The transfer function of the 25 MHz low pass Butterworth filterof FIGS. 12A and 12B is shown by the equation: $\begin{matrix}{{{T(s)} = \frac{6.25 \times 10^{14}}{s^{2} + {3.54 \times 10^{7}s} + {6.25 \times 10^{14}}}},} & (15)\end{matrix}$

[0073] while the transfer function of the 2.5 MHz filter is:$\begin{matrix}{{T^{\prime}(s)} = {\frac{6.25 \times 10^{12}}{s^{2} + {3.54 \times 10^{6}s} + {6.25 \times 10^{12}}} = {\frac{6.25 \times 10^{14}\alpha^{2}}{s^{2} + {3.54 \times 10^{7}\alpha \quad s} + {6.25 \times 10^{14}\alpha^{2}}} = {{T( \frac{s}{\alpha} )}.}}}} & (16)\end{matrix}$

[0074] In a preferred embodiment of the present invention, a filter withtwo modes of operation is proposed. In a normal operation mode (N) thefilter has transconductances with nominal values required for thefilter's primary purpose. In a test/tuning (T) operation mode, all ofthe transconductances that are significant for the transfercharacteristic of the filter are scaled by the same factor. This has theeffect of translating their frequency characteristic to lowerfrequencies, where they will be easier to measure. The scaling of thetransconductances is preferably done by current dividers placed at theoutputs of the transconductors.

[0075]FIG. 13A shows the basic building block of a testable/tunablecontinuous-time integrator, built in accordance with this invention.That is, the testable/tunable continuous-time integrator includes aplurality of the basic building blocks illustrated in FIG. 13A. Thefilter building block is an SGMAC with controllable scaling factor(CSGMAC). In a first mode of operation called a test/tuning mode, thescale factor is less than 1 (one). In a second mode of operation calleda normal mode, the scale factor is 1 (one). The CSGMAC includes aplurality of input transconductors 10, 12 . . . 1 k, havingtransconductance g_(m1), g_(m2), . . . g_(mk,) which generate currentsi_(g1)=g_(m1)*v_(in1), i_(g2)=g_(m2)*v_(in2), . . .i_(gk)=g_(mk)*v_(ink), respectively. A current adder 14 adds thecurrents i_(g1), i_(g2), . . . i_(gk), and generates a currenti_(g)=i_(g1)+i_(g2)+ . . . +i_(gk). A first switch 16, when closed,applies the current i_(g) to an input of a current divider 18, whichprovides a current i_(T) which is a fraction of input current i_(cd), atan output thereof. A second switch 20, when closed, passes the currenti_(g) directly to a very low impedance input of a current follower 22,which in turns provides output current i_(out). Capacitor 24 convertsthe output current i_(out) of current follower 22 into voltage v_(out).

[0076] In the normal mode of operation, second switch 20 is closed andfirst switch 16 is open. The current i_(g) of the current adder 14therefore passes through second switch 20 and is injected as currenti_(N) into the current follower 22. The input current to the currentfollower is thus i_(cf)=i_(N)=i_(g). In this case, the output currenti_(out) of the current follower 22 is equal to the output current of thecurrent adder 14. Incidentally, the current which flows into the outputof the current divider 18 is negligibly small.

[0077] In the test mode of operation, second switch 20 is open and firstswitch 16 is closed, so that current i_(g) is injected into the currentdivider 18 as the current i_(cd). The output current i_(T) of thecurrent divider 18 is a fraction of the input current i_(cd)=i_(g). Theoutput current i_(out) of the current follower 22 is equal to the outputcurrent of the current divider 18, or i_(out)=i_(T).

[0078] In the embodiment as illustrated in FIG. 13A, the current divider18 is a resistive current divider including first and second resistorsR₁ and R₂, similar to the resistive divider 1130 of FIG. 11. The outputcurrent of current divider 18 is:

i _(T) =R ₁/(R ₁ +R ₂)*i _(cd) <i _(cd)  (17).

[0079] Also, in the embodiment of FIG. 13A, the integrator GMACs of thetransconductance-capacitor filter are replaced with CSGMACs having thesame scaling factors. The method is exemplified in FIG. 13B for thesecond order transconductance-capacitance filter of FIG. 10.

[0080]FIG. 13B is a circuit diagram of a second order filter usingCSGMACs in the test/tuning mode according to an embodiment of thepresent invention. FIG. 13B discloses a second-order filter 1300 of thesame type presented in FIGS. 10 and 11. Filter 1300 includes athree-transconductor CSGMAC 1301 and a single-transconductor CSGMAC 1302as basic building blocks formed together in a feedback loop.

[0081] As shown in FIG. 13B, the three-transconductor CSGMAC 1301 isconfigured the same as SGMAC 1101 in FIG. 11, but additionally includesa first normal switch 1360 having a first end coupled to the output ofadder 1050 and a second end coupled to the second end of resistor R₁₂ atnode A₁. The CSGMAC 1301 further includes a first test switch 1370having a first end coupled to the output of adder 1050 and a second endcoupled to the first ends of resistors R₁₁ and R₁₂ at node A₂. Thesingle-transconductor SGMAC 1302 is configured the same as CSGMAC 1102in FIG. 11, but additionally includes a second normal switch 1365 havinga first end coupled to the output of second input transconductor 1010and a second end coupled to the second end of resistor R₂₂ at node B₁.CSGMAC 1302 further includes a second test switch 1375 having a firstend coupled to an output of second input transconductor 1010 and asecond end coupled to the first ends of resistors R₂₁ and R₂₂ at nodeB₂.

[0082] The first and second normal switches 1360 and 1365 are closedduring a normal operation mode and are opened during a testing/tuningmode. In contrast, the first and second test switches 1370 and 1375 areopen during a normal operation mode and are closed during atesting/tuning mode. As a result of this, the output current i_(g11) isinjected into the input node A₁ at the first current follower 1020through the first normal switch 1360 when in the normal mode, and intothe input node A₂ at the first resistive divider 1130 through the firsttest switch 1370 when in the test mode. Similarly, the output currenti_(g12) is injected into the input node B₁ at the second currentfollower 1025 through the second normal switch 1365 when in the normalmode, and into the input node B₂ at the second current divider 1135through the second test switch 1375 when in the test mode.

[0083] In this embodiment, the first and second resistive dividers 1130and 1135 have the same ratio, as shown in the following equation:$\begin{matrix}{\alpha = {\frac{R_{11}}{R_{11} + R_{12}} = {\frac{R_{21}}{R_{21} + R_{22}}.}}} & (18)\end{matrix}$

[0084] In the normal operation mode, the transfer function T₁₂(s) of thecircuit 1300 is shown by the equation: $\begin{matrix}{{T_{12}(s)} = {\frac{V_{out}(s)}{V_{in}(s)} = {\frac{( {g_{m1} \cdot g_{m2}} )}{{( {C_{1} \cdot C_{2}} ) \cdot s^{2}} + {( {g_{m3} \cdot C_{2}} ) \cdot s} + ( {g_{m2} \cdot g_{m4}} )}.}}} & (19)\end{matrix}$

[0085] In the test operation mode, the transfer function T′₁₂(s) of thecircuit 1300 is shown by the equation: $\begin{matrix}{{T_{12}^{\prime}(s)} = {\frac{V_{out}(s)}{V_{i\quad n}(s)} = {\frac{g_{m1} \cdot g_{m2}}{{( {\frac{C_{1}}{\alpha} \cdot \frac{C_{2}}{\alpha}} ) \cdot s^{2}} + {( {g_{m3} \cdot \frac{C_{2}}{\alpha}} ) \cdot s} + {g_{m2} \cdot g_{m4}}}.}}} & (20)\end{matrix}$

[0086] Furthermore, in the test mode, the magnitude of the frequencyresponse T₁₂(S) is scaled to lower frequencies according to thefollowing equation: $\begin{matrix}{{T_{12}^{\prime}(s)} = {{T_{12}( \frac{s}{\alpha} )}.}} & (21)\end{matrix}$

[0087] However, this low frequency response T₁₂(S) accurately reflectsthe shape of the high frequency response, and at the same time is easierto check.

[0088] In an alternate embodiment, a filter provided with the testfacility can be included in a configuration similar to that shown inFIG. 5. FIG. 14 is a block diagram showing a circuit for testing anintegrated filter using CSGMACs in the test mode, according to anotherembodiment of the present invention. FIG. 14 illustrates a testingcircuit 1400 configured similarly to the circuit of FIG. 5, with similarcircuit elements including an internal test signal source 1405, aninternal circuit 1420, first and second switches 1430 and 1435, aninternal analog-to-digital converter (ADC) 1455 and an internal digitalsignal processor (DSP) 1460, all formed on a semiconductor chip 1450.Testing circuit 1400 of FIG. 14 additionally includes circuit under test(CUT) 1415 having a test signal input T, that replaces CUT 115 of FIG.5. In FIG. 14, CUT 1415 and internal ADC 1455 are part of main circuit1470.

[0089] In the testing circuit 1400 of FIG. 14, the internal ADC 1455 ispart of the main circuit 1470, and operates with the CUT 1415 during anormal operation mode. In other words, when the switch signal SWindicates a normal mode (i.e., connecting the switches 1430 and 1435 tothe normal nodes N), the internal circuit 1420 is connected to both theADC 1455 and the CUT 1415, allowing the internal circuit 1420 to use theADC 1455 during normal operation.

[0090] In FIG. 14, test signal T is internally generated on the chip1450. As noted above, ADC 1455 is part of the main circuit 1470 and isused for test purposes as well as normal operation. In the normal modeof operation, the CUT 1415 and the ADC 1455 are connected to theinternal circuit 1420. In the test mode, the CUT 1415 is connected tothe internal test signal source 1405, the output of the ADC 1455 isprovided to the DSP 1460, and the CUT 1415 is switched to the test mode(i.e., undergoes transconductance scaling) by activating the test signalT input.

[0091] At low frequencies, required test signals can easily be generatedon the chip 1450, mostly by digital means, and the output of CUT 1415can be digitized by an existing on-chip ADC, or by low complexitydedicated low frequency measuring devices. As a result, low-frequencychecking of the filter 1415 enables an adequate evaluation of thecorrectness of the relative sizes of the capacitors, as well as therelative sizes of the transconductors. In the test/tuning mode only thetransconductances are scaled. As a result, the effect of the parasiticcapacitances (e.g., junction capacitances, wires etc.) in parallel withthe frequency setting capacitances can be accurately estimated.

[0092] One of the conventional tuning methods is the direct on-chipclosed loop approach, disclosed in FIG. 15. As shown in FIG. 15, a chip1550 includes two identical filters 1510 and 1520 that are alternativelyswitched into the normal operation path and into the tuning loop. Whenthe first filter 1510 is switched into the normal path by switches SW1and SW2 in the positions as shown in FIG. 15, the second filter 1520 isconnected to a tuning loop including control circuit 1530 and low-passfilter (LPF) 1535 by way of switches SW3, SW4 and SW6 in the positionsas shown.

[0093] That is, in the configuration as illustrated in FIG. 15, thefirst filter 1510 is provided with signal S_(in) via switch SW1 as afirst signal input I1, and outputs a first signal output O1 via switchSw2 as S_(out). Switch SW5 as illustrated is in an open position, thefirst filter 1510 having been tuned when previously switched into thetuning loop by a first transconductance tuning input G1 provided fromcontrol circuit 1530 via LPF 1535 and switch SW5 in a closed position.

[0094] The second filter 1520 is provided with a second signal input 12via switch SW3, and outputs a second signal output O2 via switch SW4.Second filter 1520 as switched into the tuning loop, is tuned with asecond transconductance tuning input G2 provided from control circuit1530 via LPF 1535 and switch SW6.

[0095] In greater detail, in FIG. 15 a reference signal Xref with anaccurate and stable frequency is applied to the control circuit 1530 andto second filter 1520 in the tuning loop, when the switches aremanipulated as illustrated. The response of second filter 1520 to thesignal Xref is a signal X0 which is compared to Xref by the controlcircuit 1530. The result of the comparison is a tuning signal Y0 whichis low-pass filtered by LPF 1535. The output of the low-pass filter 1535is signal Uc used to control the transconductance of the transconductorsof the filter to be tuned. While the first filter 1510 is in the normaloperation path and the second filter 1520 is being tuned, the signal Ucis applied to the transconductance tuning input G2 of the second filter1520 via switch SW6, until the convergence of the control signal Uc isachieved. After the control signal Uc has settled, its value is storedby the filter 1520 and the signal input 12 of the second filter 1520 isswitched via switch SW3 to the input signal Sin. After the second filter1520 has settled, the first filter 1510 is taken out of operation, thesignal output O2 of the second filter 1520 is connected via switch SW4to the output Sout and the first filter 1510 enters the tuning phase.

[0096] Accordingly, as described above, after tuning of the secondfilter 1520, the set of tuning parameters for the second filter 1520 arestored by control circuit 1530. Subsequently, switches SW1-SW6 aremanipulated into positions opposite as shown in FIG. 15, so that secondfilter 1520 is switched into the normal path for normal operation, andfirst filter 1510 is switched into the tuning loop. Incidentally,control circuit 1530 provided control of switches SW1-SW6. In thisembodiment, the tuning loop works at the normal operating frequency ofthe filter. However, the measuring technique according to the presentinvention can be used to operate the tuning loop at a lower frequency,with the advantage of having fewer critical high-frequency tuning blocksand fewer high-frequency signals active on a given chip.

[0097] The chip 1650 of FIG. 16 is configured somewhat similar to thatof FIG. 15, as including filters 1510 and 1520 which may use CSGMACs asdescribed with respect to FIG. 13B for example, switches SW1-SW4,low-pass filter (LPF) 1535 and control circuit 1530. Chip 1650additionally includes switch SW7 that connects filter 1510 to tuningparameters memory 1540 during normal operation mode and to LPF 1535during tuning operation mode. Similarly, switch SW8 connects filter 1520to tuning parameters memory 1545 during normal operation mode and to LPF1535 during tuning operation mode. Also, internal signal source 1505provides a test signal of accurate and stable frequency to controlcircuit 1530 during tuning operation mode.

[0098] Each of the first and second filters 1510 and 1520 has a normal(N) mode of operation, and a tuning (T) mode of operation. The tuningmode is similar to the test/tuning mode described previously. In thismode, the filter frequency response of filters 1510 and 1520 arescaled-down by current dividers therein that are coupled to the outputsof the transconductors within filters 1510 and 1520, under control ofsignals FS which are provided by control circuit 1530. Incidentally, thetest signal is compared to the output of the corresponding one of thefirst and second filters 1510 and 1520 that is in the tuning mode bycontrol circuit 1530, which provides the result of the comparison as thetuning signal to the corresponding filter via LPF 1535.

[0099] As shown in FIG. 16, when first filter 1510 is switched into thenormal operation path to be in the normal operation mode N by way ofswitches SW1 and SW2 as manipulated into the positions as shown, filterscaling within filter 1510 is turned off under control of signal FS andfilter 1510 is coupled to memory 1540 by way of switch SW7 in theposition as shown contacting node N. At the same time, second filter1520 is switched into the tuning loop in the tuning operation mode byway of switches SW3 and SW4 as manipulated into the positions as shown,whereby filter scaling within filter 1520 is turned on under control ofsignal FS and filter 1520 is connected to LPF 1535 by way of switch SW8in the position as shown contacting node T. Subsequently, filter 1510 isswitched into the tuning operation mode with filter scaling on andfilter 1520 is switched into the normal operation mode with filterscaling off, by way of switches SW1-SW4, SW7 and SW8 manipulated intopositions opposite as shown in FIG. 16 and control signal FS.Incidentally, the test signal generated by internal signal source 1505is provided directly to the corresponding filter in the tuning mode byway of control circuit 1530.

[0100] The invention being thus described, it will be obvious that thesame may be varied in many ways. Such variations are not to be regardedas a departure from the spirit and scope of the invention, and all suchmodifications as would be obvious to one skilled in the art are intendedto be included within the scope of the following claims.

What is claimed is:
 1. A transconductance-capacitance integratorcomprising: a plurality of transconductors that provide transconductorcurrents; an adder that adds the transconductor currents to provide atransconductor output current; a current follower that provides anoutput current; a capacitor, coupled to the current follower, thatprovides an output voltage of the transconductance-capacitanceintegrator responsive to the output current; a scaling circuit thatscales the transconductor output current by a scaling factor to providea scaled transconductor output current; and a mode switch that isoperable in a test/tuning operation mode to provide the scaledtransconductor output current to the current follower and in a normaloperation mode to provide the transconductor output current to thecurrent follower.
 2. The transconductance-capacitance integrator ofclaim 1, wherein the plurality of transconductors each have a firsttransconductance when in the normal operation mode and a secondtransconductance when in the test/tuning operation mode, the secondtransconductance being different than the first transconductance.
 3. Thetransconductance-capacitance integrator of claim 2, wherein the scalingcircuit divides the transconductor output current by the scaling factorso that the plurality of transconductors have the secondtransconductance.
 4. The transconductance-capacitance integrator ofclaim 1, wherein the scaling circuit comprises a resistive divider thatdivides the transconductor output current by the scaling factor toprovide the scaled transconductor output current.
 5. Thetransconductance-capacitance integrator of claim 1, wherein the scalingcircuit scales the transconductor output current down by the scalingfactor to provide the scaled transconductor output current.
 6. A methodof verifying a transfer function of a transconductance-capacitance basedfilter including a plurality of transconductors that provide a set oftransconductor output currents, comprising: converting the set oftransconductor output currents into a first set of output voltagesduring a normal operation mode of the transconductance-capacitancefilter; and scaling the set of transconductor output currents by ascaling factor to provide a second set of scaled output currents andconverting the second set of scaled output currents into a second set ofoutput voltages for verifying the transfer function, during atest/tuning operation mode of the transconductance-capacitance filter.7. The method of verifying a transfer function of claim 6, wherein theplurality of transconductors each have a first transconductance duringthe normal operation mode and a second transconductance during thetest/tuning operation mode, the second transconductance being differentthan the first transconductance.
 8. The method of verifying a transferfunction of claim 6, wherein said scaling comprises resistively dividingthe set of transconductor output currents to provide the second set ofscaled transconductor output currents.
 9. The method of verifying atransfer function of claim 6, wherein said scaling comprises scaling theset of transconductor output currents down to provide the second set ofscaled transconductor output currents.
 10. The method of verifying atransfer function of claim 6, wherein the set of transconductor outputcurrents are converted into the first set of output voltages and thesecond set of scaled output currents is converted into the second set ofoutput voltages by a capacitor.
 11. A direct on-chip closed loop tuningsystem comprising: a first filter having a plurality of firsttransconductors that provide a first set of transconductor currents, afirst set of adders that add the first transconductor currents of eachset to provide a first set of transconductor output currents and a firstset of scalers that scale the first set of transconductor outputcurrents to provide a scaled first set of transconductor outputcurrents, the first filter being operable in a normal operation mode tooutput the first set of tranconductor output currents and in atest/tuning operation mode to output the scaled first set oftranconductor output currents; a second filter having a plurality ofsecond tranconductors that provide a second set of transconductorcurrents, a second set of adders that add the second transconductorcurrents of each set to provide a second set of transconductor outputcurrents and a second set of scalers that scale the second set oftranconductor output currents to provide a scaled second set oftranconductor output currents, the second filter being operable in anormal operation mode to output the second set of transconductor outputcurrents and in a test/tuning operation mode to output the scaled secondset of transconductors output currents; and a controller thatsimultaneously switches one of the first and second filters into thenormal operation mode and another of the first and second filters intothe test/tuning operation mode.
 12. The direct on-chip closed looptuning system of claim 11, wherein the plurality of first and secondtransconductors each have a first transconductance when in the normaloperation mode and a second transconductance when in the test/tuningoperation mode, the second transconductance being different than thefirst transconductance.
 13. The direct on-chip closed loop tuning systemof claim 12, wherein the first and second sets of scalers respectivelyscale the first and second sets of transconductor output currents downby a scaling factor so that the plurality of first and secondtransconductors have the second transconductance.
 14. The direct on-chipclosed loop tuning system of claim 11, wherein the first and second setsof scalers each comprise a resistive divider that respectively scale thefirst and second sets of transconductor output currents down by ascaling factor to provide the scaled first and second sets oftransconductor output currents.
 15. The direct on-chip closed looptuning system of claim 11, wherein the first and second sets of scalersrespectively scale the first and second sets of transconductor outputcurrents down by a scaling factor to provide the scaled first and secondsets of transconductor output currents.